In his first meeting with President Obama, Speaker Paul D. Ryan raised concerns Tuesday about the administration’s loosening of visa waiver restrictions passed by Congress in response to the threat posed by Islamist foreign fighters traveling to the U.S.

Mr. Ryan’s office said the Wisconsin Republican “expressed concern over the administration’s implementation” of the visa waiver program.

The measure passed by Congress in December requires citizens of 38 countries participating in the visa waiver program to apply for a visa to travel to the U.S. if they have visited Iran, Syria, Sudan or Iraq since March 2011.

But Secretary of State John F. Kerry assured Iran that the administration will find ways to ensure that the changes to the U.S. visa waiver program will not interfere with Iran’s “legitimate business interests.” Iran has complained that the visa restrictions would violate its nuclear deal with the U.S.

Citing a report that more than 6,000 suspected Islamic State fighters have obtained passports from western countries, House Majority Leader Kevin McCarthy said Tuesday it proves the restrictions on the visa waiver program imposed by Congress “were as prescient as they are necessary.”

“Unfortunately, the Obama administration doesn’t see it the same way,” the California Republican said. “Under an extremely limited waiver authority granted to the administration under the law, the Department of Homeland Security is now considering granting waivers to certain categories of people who travel to such dangerous countries. The administration’s actions not only goes against the law as written and agreed to, it also puts the American people at risk.”

The Oval Office meeting with Mr. Ryan, Senate Majority Leader Mitch McConnell and Vice President Joseph R. Biden was the speaker’s first since taking the post in October.

They also discussed the Zika virus, the Trans-Pacific Partnership free trade deal, the national heroin epidemic, criminal justice reform, Puerto Rico’s debt crisis and the administration’s new task force effort to find a cure for cancer.

Ahead of the meeting, Mr. Ryan said this week that Republicans need to “channel” their anger over Mr. Obama’s ineffective leadership to craft a positive message in this election year.

“We are all angry that the country is headed in the wrong direction,” Mr. Ryan said. “We’re angry we’re not doing what we need to do to defeat [the Islamic State]. We’re angry that we have a porous border. We’re angry that people aren’t getting raises. We’re angry that we’ve had 2 percent something growth for 10 years. We’re angry that a debt crisis is on the horizon, and we’ve done nothing to fix it because of a progressive president.”

White House press secretary Josh Earnest said Republicans should have plenty of motivation in this election year to work with the president.

“There will be a lot of voters who are asking those members of Congress exactly what they’ve been doing for the last two years and what they’ve done to earn their vote, particularly when you consider that Republicans with a lot of fanfare, captured strong majorities in both houses of Congress in the last election,” he said. “The only thing that we can reliably count on appearing on the Republican legislative agenda are repeated attempts to repeal Obamacare. It does put some pressure on Speaker Ryan, Leader McConnell and other Republicans in Congress to lay out what it is exactly they support and try to find some common ground with the administration.”

After the meeting at the White House, Mr. McConnell reiterated that he has “problems” with the TPP, which the president wants Congress to pass this year over the objections of Democratic lawmakers.

“There are a number of flaws here,” Mr. McConnell said. “We’re gonna keep on talking about it and seeing if there’s a way forward.”